Counterintuitive Facts (48): Why Isn't Tomorrow's Sunrise News?
PremiumShannon Entropy: Information's essence is 'surprise.' Nonsense has zero bits
I. Suppose I want you to guess if the coin in my hand is heads or tails. How many questions do you need to ask? Only one: "Is it heads?" I answer "yes" or "no." Uncertainty is eliminated. This is called 1 Bit of information.
II. If you want to guess what number a die shows (6 possibilities). You need about 2.58 questions. log₂(6). If you want to guess which playing card I'm thinking of (52 cards). You need 5.7 questions. log₂(52). Information quantity depends on size of uncertainty.
III. But if I ask you to guess "will the sun rise tomorrow." You'll find this question boring. Because you know the answer is definitely "yes." This event's probability is nearly 100%. Uncertainty is 0. So no matter how loudly I shout this in the news, even shout it ten thousand times. The information I transmi
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